Electric motor capable of reducing cogging torque

ABSTRACT

An electric motor including a rotor including magnetic pole units and a stator including slots facing an outer peripheral surface of the rotor. Each of the magnetic pole units is bulged to an outside in a radial direction so that a waveform of a magnetic flux density generated from the rotor is a sine wave shape, and a concave part or convex part which is small enough to prevent changing of a waveform cycle of cogging torque determined by a least common multiple of the number of slots and the number of magnetic poles of the rotor, is formed at a central part in a circumferential direction of an outer peripheral surface in each of the magnetic pole units.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an electric motor capable of reducingcogging torque.

2. Description of the Related Art

In a permanent magnet electric motor that includes a rotor having apermanent magnet, due to the presence of slots of a stator core facingan outer peripheral surface of the rotor, magnetic coenergy fluctuatesduring rotation of the rotor, and therefore generates cogging torquethat is torque pulsation. The cogging torque is preferably reducedbecause the cogging torque interferes with smooth rotation of the rotorto generate sound or vibration. Conventionally, as an electric motordesigned to reduce such cogging torque, there are known electric motorsas described in Japanese Laid-open Patent Publication No. 2003-023740(JP2003-023740A) and Japanese Laid-open Patent Publication No. 11-164501(JP11-164501A).

A rotor of an electric motor described in JP2003-023740A includes amagnetic pole unit having a circular-arc outer peripheral surface bulgedto an outside in a radial direction so that a waveform of a magneticflux density generated from the rotor is a sine wave shape. Maximumouter diameter parts of the outer peripheral surface are arranged onboth sides of a circumferential direction center (magnetic pole center)of the magnetic pole unit, and a concave part is formed in thecircumferential direction center of the magnetic pole unit. Thisarrangement doubles the number of waveform peaks of cogging torquegenerated for each rotation of the rotor and reduces a magnitude of thecogging torque by half. On the other hand, JP11-164501A describes anelectric motor in which an outer peripheral surface of a magnetic poleunit of a rotor is formed into a cylindrical shape around a rotary shaftof the rotor. This electric motor is configured such that a waveform ofa magnetic flux density of the rotor is not a sine wave shape but atrapezoidal wave shape.

The electric motor described in JP2003-023740A is configured to reducethe magnitude of cogging torque by half, by substantially doubling thenumber of magnetic poles, but is unable to adjust the magnitude of thecogging torque to an arbitrary magnitude.

SUMMARY OF THE INVENTION

According to an aspect of the present invention, an electric motorincludes a rotor including magnetic pole units, and a stator includingslots facing an outer peripheral surface of the rotor. Each of themagnetic pole units is bulged to an outside in a radial direction sothat a waveform of a magnetic flux density generated from the rotor is asine wave shape. A concave part or convex part is formed at a centralpart in a circumferential direction of an outer peripheral surface ineach of the magnetic pole units, and is small enough to prevent changingof a waveform period of cogging torque determined by a least commonmultiple of the number of slots and the number of magnetic poles of therotor.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects, features, and advantages of the present invention willbecome clearer from the following description of embodiments in relationto the attached drawings. In the attached drawings,

FIG. 1 is a sectional view schematically illustrating an internalconfiguration of an electric motor according to an embodiment of thepresent invention;

FIG. 2A is an enlarged view illustrating a rotor illustrated in FIG. 1;

FIG. 2B is an enlarged view illustrating a configuration of one pole ofthe rotor illustrated in FIG. 2A;

FIG. 3 is a diagram illustrating a waveform of a magnetic flux densitywhen it is assumed that no slot opening is formed in an inner peripheralsurface of a stator;

FIG. 4 is a diagram illustrating an example of magnetic flux lines in anelectric motor;

FIG. 5 is a diagram illustrating a waveform of a magnetic flux densitywhen a slot opening is formed in the inner peripheral surface of thestator;

FIG. 6 is an enlarged view illustrating an outer peripheral surfaceshape of the rotor constituting the electric motor according to theembodiment of the present invention;

FIG. 7 is a diagram illustrating a change in waveform of cogging torquegenerated in the electric motor having the outer peripheral surfaceshape illustrated in FIG. 6;

FIG. 8 is a diagram illustrating a change in waveform of cogging torquewith changes of a maximum correction amount;

FIG. 9A is a diagram illustrating a rotor having a circular outerperipheral surface;

FIG. 9B is a diagram illustrating a waveform of a magnetic flux densitygenerated from the rotor illustrated in FIG. 9A;

FIG. 10 is a diagram illustrating a change in waveform of cogging torquegenerated in the electric motor having the outer peripheral surfaceshape illustrated in FIG. 9A;

FIG. 11 is a diagram illustrating a modified example of the electricmotor illustrated in FIG. 6;

FIG. 12 is a diagram illustrating change in waveforms of cogging torquegenerated in the electric motor having an outer peripheral surface shapeillustrated in FIG. 11;

FIG. 13 is a diagram illustrating another modified example of theelectric motor illustrated in FIG. 6;

FIG. 14 is a diagram illustrating further modified example of theelectric motor illustrated in FIG. 6;

FIG. 15A is a diagram describing a method for setting of an outerperipheral surface shape of a rotor;

FIG. 15B is an enlarged view illustrating the outer peripheral surfaceshape of the rotor obtained by the method illustrated in FIG. 15A;

FIG. 16 is a diagram illustrating further modified example of theelectric motor illustrated in FIG. 6;

FIG. 17 is a diagram illustrating a change in waveform of cogging torquegenerated in the electric motor having an outer peripheral surface shapeillustrated in FIG. 16;

FIG. 18 is a diagram illustrating a modified example of the electricmotor illustrated in FIG. 2A;

FIG. 19 is a diagram illustrating a modified example of the electricmotor illustrated in FIG. 1;

FIG. 20 is a diagram illustrating a change in waveform of cogging torquegenerated in the electric motor illustrated in FIG. 19; and

FIG. 21 is a diagram illustrating an example of magnetic flux lines inan electric motor according to further modified example of the electricmotor illustrated in FIG. 1.

DETAILED DESCRIPTION

Hereinafter, the embodiments of the present invention will be describedreferring to FIGS. 1 to 21. FIG. 1 is a sectional view schematicallyillustrating an internal configuration of an electric motor 100according to an embodiment of the present invention. The electric motor100, which is a permanent magnet synchronous electric motor with eightpoles and twelve slots, includes a rotor 1 provided with permanentmagnets 3 and a stator 2 disposed around the rotor 1. An output shaft 4is disposed at a center of the rotor 1.

Predetermined space is formed between an outer peripheral surface 11 ofthe rotor 1 and an inner peripheral surface 21 of the stator 2. In theinner peripheral surface 21 of the stator 2, slot openings 22 and teeth23 are alternately formed in a circumferential direction. Slots 20 areformed on radial direction outsides of the slot openings 22. A coil isreceived in each slot 20. By supplying current to the coil, the stator 2forms a rotating magnetic field, and the rotor 1 is rotated insynchronization with the rotating magnetic field.

FIG. 2A is an enlarged view illustrating the rotor 1. As illustrated inFIG. 2A, the eight permanent magnets 3 are radially arranged at equalintervals in a circumferential direction around a rotational center P0of the rotor 1. Each yoke 10 is disposed between the permanent magnets3, 3 adjacent to each other in the circumferential direction, and eightmagnetic poles (magnetic pole units) having the same shape are formed bythe yokes 10. The yokes 10 are configured by stacking a plurality ofplate members in an axial direction and integrally fastening them viatie rods 5.

FIG. 2B is an enlarged view illustrating a configuration of a singleyoke 10, in other words, the rotor 1 of one pole, illustrated in FIG.2A. In FIG. 2B, a central angle of the rotor 1 is 45°. The rotor 1 has aline-symmetrical shape in the circumferential direction with respect toa reference line L0 connecting the rotational center P0 with acircumferential-direction center (magnetic pole center P1) of an outerperipheral surface 11 of the yoke 10 by a straight line. The outerperipheral surface 11 of the yoke 10 is formed to bulge to an outside ina radial direction. Accordingly, a distance (rotor radius R) from therotational center P0 to the outer peripheral surface 11 of the yoke 10is smaller as an angle θ from the straight line L0 is larger. The rotorradius R is maximum at a magnetic pole central part 12 in which θ is 0°.An angle θ from the reference line L0 around the rotational center P0 isalso referred to as a mechanical angle.

FIG. 3 is a diagram illustrating a waveform of a magnetic flux density Bwhen it is assumed that no slot opening 22 is formed in an innerperipheral surface 21 of the stator 2. This waveform is obtained bydisposing a cylinder around the rotor 1 and measuring a magnetic fluxbetween the rotor 1 and the cylinder in a static state of the rotor 1.In FIG. 3, a horizontal axis indicates a mechanical angle of the rotor 1while a vertical axis indicates a radial-direction component of themagnetic flux density B generated from the rotor 1. One cycle of thewaveform corresponds to a mechanical angle 45°. In the embodiment, therotor 1 has the outer peripheral surface 11 bulged to the radialdirection outside. Thus, as illustrated in FIG. 3, the magnetic fluxdensity B generated from the rotor 1 is a sine wave shape, and themagnetic flux concentrates at the magnetic pole central part 12(illustrated as an in FIG. 3).

The real electric motor 100 includes the slot openings 22 formed in theinner peripheral surface 21 of the stator 2. Thus, a difference isgenerated in magnetic permeability μ between the slot openings 22 andthe teeth 23. In other words, magnetic permeability μ of the teeth 23composed of an electromagnetic steel sheet is generally larger by 1000times or more than magnetic permeability μ of the slot openings 22determined by air and a coil (copper) in each slot 20. As a result, asillustrated in FIG. 4, the magnetic flux generated from the rotor 1passes through the teeth 23 without passing through the slot openings 22having high magnetic resistance. In other words, the magnetic flux isdense at the teeth 23, thus generating a coarse/fine distribution of themagnetic flux density B in the circumferential direction.

A physical amount obtained by magnetic flux density B×B/magneticpermeability μ is referred to as magnetic coenergy. When the magneticpole central part 12 sequentially passes through the vicinities of theslot openings 22 and the teeth 23 with rotation of the rotor 1, themagnetic coenergy of the magnetic pole central part 12 fluctuates, thusgenerating cogging torque that is torque pulsation. A generation statusof the cogging torque will be described specifically. FIG. 5 is adiagram illustrating a waveform of the magnetic flux density B when slotopenings 22 are formed in the inner peripheral surface 21 of the stator2.

As illustrated in FIG. 5, at a position where the rotor 1 faces any ofthe slot openings 22 (“b” illustrated in FIG. 5), the sine wave shape isbroken, and the magnetic flux density B approaches 0. The magneticcoenergy accordingly fluctuates to generate cogging torque. The coggingtorque is generated by a number of times equal to a least commonmultiple of the number of slots and the number of magnetic poles foreach rotation of the rotor 1 (for example, twenty four times for thecase of eight poles and twelve slots), and a mechanical angle of a cycleof the cogging torque is 15° (=360°/24). The cogging torque ispreferably reduced because it interferes with smooth rotation of therotor 1 to generate sound or vibration. In the embodiment, to reducesuch cogging torque, the magnetic pole central part 12 of the rotor 1(yoke 10) where the magnetic flux concentrates is configured asdescribed below.

FIG. 6 is an enlarged view illustrating an outer peripheral shape of theyoke 10 constituting the electric motor 100 according to the embodimentof the present invention. A horizontal axis indicates an angle from thereference line L0 (illustrated in FIG. 2B), in other words, a mechanicalangle θ, while a vertical axis indicates a distance from the rotationalcenter P0 to the outer peripheral surface 11, in other words, a rotorradius R. In the embodiment, the outer peripheral surface 11 (indicatedby a solid line) is set by adding a correction amount ΔR in the radialdirection using a mechanical angle θ as a parameter to a referencesurface 11A (indicated by dotted line) using a mechanical angle θ as aparameter.

The reference surface 11A is bulged to an outside in the radialdirection so that the rotor radius R is maximum R1 at the magnetic polecenter P1 of the mechanical angle 0°, and is formed into a circular arcshape as a whole. A waveform of the magnetic flux density B from thereference surface 11A has a sine wave shape as illustrated in FIG. 3when the presence of the slots 20 is ignored. The rotor radius R of thereference surface 11A is set by the following formula (I):

R=a−b/cos(Cθ)   (I)

In the formula (I), “a” is a radius (stator inner diameter) of the innerperipheral surface 21 of the stator, “b” is a minimum gap between therotor 1 and the stator 2, and c is a coefficient. The mechanical angle θis set within a range of −7.5° to 7.5°.

The rotor radius R of the outer peripheral surface 11 is set by thefollowing formula (II):

R=a−b/cos(cθ)+d×sin(eθ)   (II)

In the formula (II), d×sin(eθ) is a correction function indicating acorrection amount ΔR, “d” is a maximum correction amount, and “e” is acoefficient indicating characteristics of the correction function. Forexample, the coefficient “e” is set so that eθ can be respectively 180°and -180° when the mechanical angle θ is maximum and minimum. At thistime, the correction amount ΔR is θ.

By setting the correction amount ΔR based on the sine function asdescribed above, the correction amount ΔR at the magnetic pole center P1(θ=0) is 0, and the correction amount AR gradually increases with theincrease of the mechanical angle θ. Accordingly, a tiny and smoothcircular-arc concave part 15 is formed at the magnetic pole central part12. A ratio b/a of the minimum gap “b” to the stator inner diameter “a”is, for example, about 1/10, and a ratio d/b of the maximum correctionamount “d” to the minimum gap “b” is, for example, about 1/10. Thus, aratio d/a of the maximum correction amount “d” to the stator innerdiameter “a” is about 1/100, and the maximum correction amount “d” isconsiderably smaller than the stator inner diameter “a”.

In this example, an absolute value of the maximum correction amount “d”is, for example, 0.1 mm or less. Visual checking of the presence ofcorrection is consequently difficult. Checking can be performed by usinga measuring device such as an optical projector. Strictly, the maximumcorrection amount “d” is set according to the size of the stator innerdiameter “a” and the size of the minimum gap “b”. The maximum correctionamount “d” is larger as the stator inner diameter “a” and the minimumgap “b” are larger. For example, the maximum correction amount “d” iswithin a range of 0.01 mm to 0.1 mm.

FIG. 7 is a diagram illustrating a waveform of cogging torque. In FIG.7, W0 is a waveform of cogging torque when no correction is performedfor the reference surface 11A, in other words, when the rotor radius Ris set along the dotted line illustrated in FIG. 6. W1 is a waveform ofcogging torque when correction is performed for the reference surface11A, in other words, when the rotor radius R is set along the solid lineillustrated in FIG. 6. As illustrated in FIG. 7, the cogging torqueindicated by the waveform W1 is smaller than that indicated by thewaveform W0. Thus, a size of the cogging torque can be reduced by addingthe correction amount ΔR to the rotor radius R of the reference surface11A to form the tiny concave part 15 at the magnetic pole central part12.

FIG. 8 is a diagram illustrating a change in waveform of cogging torquewith changes of the maximum correction amount “d”. Waveforms W11, W12,W13, W14, and W15 are waveforms of cogging toque corresponding tomaximum correction amounts d1, d2, d3, d4, and d5, respectively. Themaximum correction amounts d1 to d5 are set in a relationship ofd1<d2<d3<d4<d5. As illustrated in FIG. 8, with the increase of themaximum correction amount “d”, the cogging torque deviates from thewaveform W0, and peak values of the cogging torque approach 0(W11→W12→W13). When the maximum correction amount “d” increases more,waveforms (W14 and W15) of opposite phases are generated. Thus, bysetting the maximum correction amount “d” to an optimal value, thecogging torque can be reduced to the utmost extent. In this case, themaximum correction amount “d” is very small (e.g., 0.1 mm or less). As aresult, even when the maximum correction amount “d” is changed, noinfluence is given to the waveform cycle of the cogging toque, but onlythe magnitude of the cogging torque can be changed.

The present embodiment can provide the following operation effects.

(1) Each of the magnetic pole units (yokes 10) of the rotor 1 of theelectric motor 100 is bulged to the radial direction outside so that thewaveform of the magnetic flux density B generated from the rotor 1 is asine wave shape (illustrated in FIG. 3), and the tiny concave part 15(illustrated in FIG. 6) is formed at the central part in thecircumferential direction (magnetic pole central part 12) of the outerperipheral surface 11 of the magnetic pole unit, which is small enoughto prevent changing of the waveform cycle of the cogging torquedetermined by the least common multiple of the number of slots 20 andthe number of magnetic poles of the rotor 1. Thus, the cogging torquecan be greatly reduced while keeping the waveform cycle of the coggingtorque constant.

Specifically, in a configuration where convex parts are formed on bothsides of the magnetic pole center P1 to substantially double the numberof magnetic poles of the rotor 1, the waveform cycle of the coggingtorque is reduced to be about half. As a result, while the magnitude ofthe cogging torque would be about half, reduction of the magnitude ofthe cogging torque of more than half is difficult. On the other hand, asin the case of the embodiment, when the tiny concave part 15 visuallyindiscernible are formed at the magnetic pole center 12 where themagnetic flux concentrates, the magnitude of the cogging torque can bereduced to the utmost extent by appropriately adjusting the correctionamount ΔR (maximum correction amount “d”) determining the concave part15.

The aforementioned effect can be obtained in the case of the rotor 1configured such that the rotor radius R of the reference surface 11A ismaximum at the magnetic pole central part 12 and the waveform of themagnetic flux density generated from the rotor 1 exhibits the sine waveshape. For example, as illustrated in FIG. 9A, when an outer peripheralsurface 111 of a rotor 101 has a circular shape, a waveform of amagnetic flux density B generated from the rotor 101 has a trapezoidalshape illustrated in FIG. 9B. FIG. 10 is a diagram illustrating a changein waveform of cogging torque when a correction amount ΔR is added tothe reference surface 11A as in the aforementioned case, with the outerperipheral surface 111 of the rotor 101 set as the reference surface11A. In FIG. 10, a waveform W100 is a waveform of cogging torque when nocorrection is performed for the reference surface 11A. Each of waveformsW101 and W102 is a waveform when correction is performed.

In the case of the trapezoidal wave, no magnetic flux concentrates atmagnetic pole centers (illustrated in FIG. 9B). Thus, as illustrated inFIG. 10, a reduction effect of cogging torque is not obtained even ifcorrection is performed to form concave parts at the magnetic polecentral parts. On the other hand, in the case of the sine wave as in theembodiment, the magnetic flux concentrates at the magnetic pole centralparts 12. Thus, by forming the tiny concave parts 15 at the magneticpole central parts 12, magnetic coenergy can be adjusted, and thecogging torque can be reduced.

(2) When the maximum correction amount “d” is set, for example, equal toor less than 0.1 mm, or about 1/100 of the stator inner diameter “a”,the correction amount ΔR is very small, and the magnitude of the coggingtorque can be adjusted according to the maximum correction amount “d”without changing the cycle of the cogging torque. In other words, whenthe magnetic pole center 12 where the magnetic flux concentrates isformed into a concavo-convex shape of about several mm in height, aninfluence on the magnetic pole unit is large, thus causing a change ofthe cycle of the cogging torque. On the other hand, when the maximumcorrection amount “d” is very small, a shape change of the magnetic poleunit is little, and only the magnitude of the cogging torque can beappropriately adjusted.

(3) The shape of the outer peripheral surface 11 of the magnetic poleunit, in other words, the radius R from the rotor rotational center P0to the outer peripheral surface 11, is set by adding the radialdirection correction amount ΔR to the reference surface 11A bulged tothe radial direction outside so that the waveform of the magnetic fluxdensity B generated from the rotor 1 exhibits the sine wave shape. Thus,shape setting of the outer peripheral surface 11 is easy.

(4) The concave part 15 is formed to have a smooth curve at the magneticpole central part 12. Thus, without any sudden change of the shape ofthe outer peripheral surface 11 in the circumferential direction,fluctuation of the magnetic coenergy caused by the presence of theconcave part 15 can be suppressed.

(5) The correction amount ΔR is set based on the function using, as theparameter, the phase in which the circumferential-direction center ofthe magnetic pole unit is 0°, in other words, the function using, as theparameter, the mechanical angle θ from the reference line L0 passingthrough the magnetic pole center P0. Thus, setting of the correctionamount ΔR changed with the increase of the mechanical angle θ is easy.

(6) The correction amount ΔR is set by using the sine function. Thus,the concave part 15 with a smooth shape can be easily formed at themagnetic pole central part 12.

(7) When the least common multiple of the number of magnetic poles andthe number of slots is increased (e.g., larger than 100), the cycle ofthe cogging torque is shortened to enable reduction of the magnitude ofthe cogging torque, but the number of slots 20 or magnets 3 increases.In this regard, according to the embodiment, the cogging torque isreduced by forming the tiny concave part 15 at the magnetic pole centralpart 12. This eliminates the necessity of increasing the least commonmultiple of the number of magnetic poles and the number of slots (in theembodiment, least common multiple is 24), and the number of slots 20 ormagnets 3 can be reduced.

(Modified Example)

In the above embodiment, the correction amount ΔR of the outerperipheral surface 11 of the magnetic pole unit in the radial directionis set by using the sine function. However, the correction amount ΔR canbe set by using a cosine function or a hyperbolic cosine function. Forexample, the rotor radius R of the reference surface 11A may be given bythe above formula (I), and a rotor radius R after correction may be setby the following formula (III):

R=a−(b−d)/cos(cθ)+d/cosh(eθ)   (III)

In the formula (III), 1/cosh(θ)=1 is satisfied when θ=0. Accordingly, tomatch a minimum gap “b” after correction with a minimum gap “b” of thereference surface 11A, 1/cos(cθ) is multiplied not by a coefficient “b”but by a coefficient (b-d).

FIG. 11 is an enlarged view illustrating an outer peripheral shape ofthe yoke 10 obtained by the above formula (III). A dotted line in FIG.11 is, as in the case illustrated in FIG. 6, a rotor radius R of thereference surface 11A. As indicated by a solid line in FIG. 11, a tinyconcave part 15 is formed at the magnetic pole central part 12. Acorrection amount ΔR at the magnetic pole center 21 is 0, and theminimum gap “b” is not changed before and after correction.

FIG. 12 is a diagram illustrating a waveform of cogging torque when theouter peripheral surface 11 of the rotor 1 is configured as illustratedin FIG. 11. In FIG. 12, W0 and W1 are respectively a waveform when nocorrection is performed for the reference surface 11A (indicated by thedotted line in FIG. 11) and a waveform when correction is performed(indicated by the solid line in FIG. 11). As illustrated in FIG. 12, thecogging torque indicated by the waveform W1 is smaller than thatindicated by the waveform W0. Thus, a magnitude of the cogging torquecan be reduced by adding the correction amount ΔR to the rotor radius Rof the reference surface 11A to form the tiny concave part 15 at themagnetic pole central part 12.

In the above embodiment, the tiny concave part 15 is formed at themagnetic pole central part 12 of the rotor 1. However, a tiny convexpart may be formed instead. FIG. 13 is a diagram illustrating an examplewhere a tiny convex part 16 is formed. In FIG. 13, a rotor radius R(indicated by a solid line in FIG. 13) is set by the following formula(IV):

R=a−b/cos(cθ)+d/cosh(eθ)   (IV)

In this case, 1/cosh(0)=1 is satisfied when θ=0. Thus, the rotor radiusR is larger by a maximum correction amount “d” than that of thereference surface 11A, and a minimum gap is accordingly smaller by acorresponding amount. However, because the maximum correction amount “d”is very small, a changing amount of the minimum gap is small, causing noproblem for gap setting for rotor rotation. When the tiny convex part 16is formed at the magnetic pole central part 12, the minimum gap aftercorrection may be matched with the minimum gap “b” before correction.

The tiny concave part 15 or the tiny convex part 16 may be formed at themagnetic pole central part 12 by using a spline function. FIG. 14 is adiagram illustrating an example where a tiny concave part is formed atthe magnetic pole central part 12 by using the spline function. Thespline function is obtained by arbitrarily providing a sequence ofpoints and sequentially connecting the points. For example, when theconcave part 15 is formed by using the sine function, the sequence ofpoints may be given along a sine curve and the points may be connectedby the spline function.

The tiny concave part 15 or the tiny convex part 16 may be formed at themagnetic pole central part 12 without using any of the aforementionedfunctions. For example, as illustrated in FIG. 15A, the referencesurface 11A is rotated clockwise by only a predetermined angle θ1 (e.g.,10°) around the rotational center P0 of the rotor 1 to obtain a firstcurved surface S1. In addition, the reference surface 11A is rotatedanticlockwise by only a predetermined angle −θ1 to obtain a secondcurved surface S2. Alternatively, the first curved surface S1 issymmetrically folded at the axis L0 to obtain the second curved surfaceS2. By smoothly connecting the first curved surface S1 and the secondcurved surface S2 at the magnetic pole central part 12, the tiny concavepart 15 can be formed as illustrated in FIG. 15B.

As apparent from the foregoing, the most remarkable feature of thepresent invention is that the tiny concave part 15 or the tiny convexpart 16 is formed at the magnetic pole central part 12. In this case,“tiny” means a size enough to prevent changing of the waveform cycle ofthe cogging torque determined by the least common multiple of the numberof slots 20 and the number of magnetic poles of the rotor 1. Forexample, such size includes a depth of 0.1 mm or less for a concave partor a height of 0.1 mm or less for a convex part. Sizes of the concavepart 15 and the convex part 16 are preferably set according to the outerdiameter of the rotor 1 or the size of the minimum gap “b” instead ofsetting uniformly ignoring the size of the electric motor.

In the embodiment, the shape of the outer peripheral surface 11 of therotor 1 is set based on the distance R from the rotational center P0 ofthe rotor 1. However, for example, as illustrated in FIG. 16, the shape(reference surface 11 a and correction amount ΔR) of the outerperipheral surface 11 of the rotor 1 may be set based on a distance Rfrom a point P2 offset from the rotational center P0. In other words, areference point P2 that is a reference for shape setting of the outerperipheral surface 11 may be set at a position shifted from therotational center P0.

FIG. 17 is a diagram illustrating a waveform of cogging torque withrespect to the outer peripheral surface 11 illustrated in FIG. 16. InFIG. 17, W0 is a waveform when the reference surface 11 a is an outerperipheral surface 11, and W1 is a waveform when the outer peripheralsurface 11 is set by adding a correction amount ΔR to the referencesurface 11 a to form the tiny concave part 15 at the magnetic polecentral part 12. As illustrated in FIG. 17, even when the referencepoint P2 of the outer peripheral surface 11 is not at the rotationalcenter P0, the cogging torque can be reduced by forming the tiny concavepart 15 at the magnetic pole central part 12.

In the above embodiment, the magnets 3 are radially arranged in therotor 1 to form the magnetic pole units (illustrated in FIG. 2A).However, the arrangement of the magnets 3 is not limited to this as longas the magnetic pole units are bulged to the outside in the radialdirection so that the waveform of the magnetic flux density B generatedfrom the rotor 1 is a sine wave shape. For example, as illustrated inFIG. 18, the magnets 3 may be buried along the circumferential directionof the rotor 1 to constitute an internal buried rotor 1. Alternatively,the magnets may be stuck to a surface of the rotor 1. In the exampleillustrated in FIG. 18, an outer peripheral surface 11 of the rotor 1 isset by using a hyperbolic cosine function (cosh function). In this case,as in the case illustrated in FIG. 17, cogging torque can be reduced byforming a tiny concave part 15 at the magnetic pole central part 12.

The embodiment has been directed to the electric motor 100 with eightpoles and twelve slots. However, the number of magnetic poles and thenumber of slots of the electric motor to which the present invention isapplied are not limited to these numbers. For example, the presentinvention can be similarly applied to an electric motor 100A with eightpoles and thirty six slots illustrated in FIG. 19. FIG. 20 is a diagramillustrating a waveform of cogging torque when the present invention isapplied to the electric motor 100A illustrated in FIG. 19. In FIG. 20,as in the case illustrated in FIG. 7, waveforms W0 and W1 arerespectively waveforms before and after tiny concave parts 15 are formedat the magnetic pole central parts 12. As illustrated in FIG. 20, thecogging torque can be reduced by forming the tiny concave parts 15 atthe magnetic pole central parts 12.

FIG. 21 is a diagram illustrating magnetic flux lines in an electricmotor 100B with ten poles and twelve slots. The present invention can besimilarly applied to the electric motor 100B with ten poles and twelveslots. A generation number of times of cogging torque per rotation ofthe rotor 1 is determined by a least common multiple of the number ofmagnetic poles and the number of slots. However, according to thepresent invention, the cogging torque can be reduced even withoutincreasing the least common multiple. Thus, the least common multiple ispreferably 100 or less.

The embodiment can be arbitrarily combined with one or a plurality ofmodified examples.

According to the present invention, the concave or convex parts areformed at the central part in the circumferential direction of the outerperipheral surfaces of the magnetic pole units, and the concave orconvex parts are small enough to prevent changing of the waveform cycleof the cogging torque determined by the least common multiple of thenumber of slots and the number of magnetic poles of the rotor. Thus, byappropriately changing the sizes of the concave or convex parts, themagnitude of the cogging torque can be easily adjusted to an arbitrarymagnitude.

While the present invention has been described with reference to thepreferred embodiments thereof, it will be understood, by those skilledin the art, that various changes and modifications may be made theretowithout departing from the scope of the appended claims.

1. An electric motor comprising: a rotor including magnetic pole units;and a stator including slots facing an outer peripheral surface of therotor, wherein, each of the magnetic pole units is bulged to an outsidein a radial direction so that a waveform of a magnetic flux densitygenerated from the rotor is a sine wave shape, and a concave part orconvex part is formed at a central part in a circumferential directionof an outer peripheral surface in each of the magnetic pole units, theconcave part or convex part being small enough to prevent changing of awaveform cycle of cogging torque determined by a least common multipleof the number of slots and the number of magnetic poles of the rotor. 2.The electric motor according to claim 1, wherein a depth of the concavepart or a height of the convex part is equal to or less than 0.1 mm. 3.The electric motor according to claim 1, wherein the outer peripheralsurface of each of the magnetic pole units is set by adding a correctionamount in the radial direction to a reference surface bulged to theoutside in the radial direction so that the waveform of the magneticflux density generated from the rotor is the sine wave shape.
 4. Theelectric motor according to claim 3, wherein the correction amount isset so that the concave part or the convex part is formed with a smoothcurve.
 5. The electric motor according to claim 3, wherein thecorrection amount is set based on a function using, as a parameter, aphase in which a center in the circumferential direction of each of themagnetic pole units is 0°.
 6. The electric motor according to claim 5,wherein the function is any one of a sine function, a cosine function,and a hyperbolic cosine function.
 7. The electric motor according toclaim 1, wherein the least common multiple of the number of magneticpoles of the rotor and the number of slots is equal to or less than 100.